Comparison of Numerical Solutions by TVD Schemes in Simulations of Irregular Waves Propagating over a Submerged Shoal Using FUNWAVE-TVD Numerical Model

摘要

Numerical convergence and stability of TVD schemes have been applied in the FUNWAVE-TVD model were compared.The fourth order accurate MUSCL-TVD scheme using minmod limiter suggested by Yamamoto and Daiguji (1993),the fourth order accurate MUSCL-TVD scheme using van-Leer limiter suggested by Erduran et al.(2005) and the second order accurate MUSCL-TVD scheme using van-Leer limiter in Zhou et al.(2001) were compared.Comparisons of the numerical scheme were conducted with experimental data of Vincent and Briggs irregular wave experiments.In comparison with the fourth order accurate scheme using van-Leer limiter,the fourth order accurate scheme using minmod limiter is less dissipative but required lower CFL condition for stable numerical solution.On the other hand,the scheme using van-Leer limiter required smaller resolution spatial grid due to numerical dissipation,but relatively higher CFL condition can be used compared to the scheme using minmod limiter.In the breaking wave experiments which were conducted using high resolution spatial grid to reduce numerical dissipation,the characteristic of the schemes can be clearly observed.Numerical instabilities and blow-up of the numerical solutions were found in the irregular wave breaking simulation with the scheme using minmod limiter.However,the simulation can be completed with the scheme using van-Leer limiter,but required low CFL condition.Good agreements with the observed data were also observed in the results using van-Leer limiter.